Decision Science Letters

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1 Decision Science Leers (3) 9 4 Conens liss available a GrowingScience Decision Science Leers homepage: Esimaing he risk-reurn radeoff in MENA Sock Markes Salim Lahmiri * ESCA School of Managemen, Casablanca, Morocco & Deparmen of Compuer Science, Universiy of Quebec a Monreal, Monreal, Canada C H R O N I C L E A B S T R A C T Aricle hisory: Received Ocober, Acceped January, 3 Available online January 3 Keywords: MENA Sock Markes GARCH-M Economerics This sudy employs he generalized auoregressive condiionally heeroskedasic in he mean (GARCH-M) mehodology o invesigae he reurn generaing process of Jordan, Kingdom of Saudi Arabia (KSA), Kuwai, and Morocco sock marke indices. The radeoff beween reurns and he condiional variance is found o be posiive in all markes. In oher words, he empirical findings show ha invesors are rewarded for heir exposure o more risk in hese financial markes. This resul is consisen wih boh financial heory and empirical finance. 3 Growing Science Ld. All righs reserved.. Inroducion Since early works of Meron (973, 98), he risk-reurn relaionship has become an imporan concern for invesors and academicians. In equilibrium, addiional risk aken by an invesor should be compensaed hrough higher expeced reurn. As a resul, risk and reurn are expeced o be posiively relaed. The GARCH-in-Mean (generalized auoregressive condiionally heeroskedasic in he mean: GARCH-M) of Engle e al. (987) is he mos common model o evaluae he ime-varying riskreurn relaionship (French e al., 987; Campbell & Henschel, 99; Bansal & Lundblad, ; Girard e al., ; Xing & Howe, 3; Baillie & DeGennaro, 99; Glosen e al., 993; Nam e al., ). The GARCH-M model allows he inroducion of he condiional variance, or some funcion of i, as a regressor in he mean equaion. Thus, he validiy of he posiive relaionship beween risk and reurn can saisically be esed. The empirical lieraure using GARCH-M repored conflicing findings. In oher words, empirical lieraure examining his issue is no unanimous. For insance, Baillie and DeGennaro (99), Glosen e al. (993), and Nam e al. () have repored a negaive * Corresponding auhor. addresses: slahmiri@esca.ma & lahmiri.salim@courrier.uqam.ca (S. Lahmiri) 3 Growing Science Ld. All righs reserved. doi:.567/j.dsl.3..

2 relaionship beween risk and reurn, whils French e al. (987), Campbell and Henschel (99), Bansal and Lundblad (), Girard e al. (), and Xing and Howe (3) have repored a posiive relaionship. Mos of previous works examined he risk-reurn radeoff in developed counries (French e al., 987; Campbell & Henschel, 99; Bansal & Lundblad, ; Girard e al., ; Xing & Howe, 3; Baillie & DeGennaro, 99; Glosen e al., 993; Nam e al., ), and a lile aenion has been paid o developing counries (Curci e al., ; Forgha, ). The purpose of his paper is o invesigae he risk-reurn radeoff in he Middle Eas and Norh Africa (MENA) mos acive sock markes; namely Jordan, Kingdom of Saudi Arabia (KSA), Kuwai, and Morocco. The ARMA- GARCH-M (Auoregressif moving average: ARMA, see Box e al., 994) process is employed o conduc his empirical sudy. The ouline of he res of he paper is as follows. The nex secion briefly describes he daa and he ARMA-GARCH-M model and provides he resuls. The concluding secion summarizes he findings.. Daa, esimaion, and resuls The daa employed in his applicaion consis of daily observaions on Jordan, Kingdom of Saudi Arabia (KSA), Kuwai, and Morocco marke sock marke indices. The overall sample covers he period July h 6 o December h for Jordan, January 6 h 7 o December h for KSA, June 7 h o December h for Kuwai, and he period from December 8 h 8 o November 3h for Morocco. The daily coninuously compounded percenage reurns (r ) are defined as he firs differences of he naural logarihmic price levels, i.e. r = log(p )-log(p - ) where P is he closing price level of he sock marke index, and is he ime scrip. The price level and reurns of each marke are shown in Figures.a o.d, where he x-axis refers o observaions. 6 Price Level Price Level Fig..a Series of Jordanian sock marke price level and reurns.5 x 4 Price Level Fig..b Series of Saudi sock marke price level and reurns.4 x 4 Price Level Fig..c Series of Kuwaii sock marke price level and reurns Fig..d Series of Casablanca sock marke price level, reurns, and volailiy The descripive saisics of reurn series (r ) are given Table. In each marke, he reurns are found o be less volaile given he low value of sandard deviaion. In addiion, he disribuion of he reurns

3 S. Lahmiri / Decision Science Leers (3) series is negaively skewed in Jordan, KSA, and Kuwai. The Jarque-Bera saisic is highly saisically significan a he 5 percen significance level, indicaing ha he null hypohesis of normally disribued reurns series is rejeced in all markes. The null hypohesis of non-saionariy (uni roo) of reurn series is esed using he Augmened Dickey Fuller (ADF) (Dickey and Fuller, 979) and Philipps and Perron (988) uni roo ess. Boh he ADF and PP show ha he daily reurns series of all markes follow saionary processes (See reurn series in Figures.a o.d). The Ljung Box-Q (LB-Q) (Ljung and Box, 978) saisics are compued o es for serial correlaion in he reurns series. In all markes, he LB-Q saisics are highly saisically significan a he 5 percen level. As a resul, he null hypohesis of no auocorrelaion in he reurns series is rejeced. A firs sigh, all markes daily reurns in Figures.a o.d show ha he mean reurns are consan bu he variances change over ime suggesing ha he volailiies end o cluser. In sum, he preliminary analysis shows ha all markes daily reurns exhibi means reversion and irregular ime-varying volailiies. Thus, a GARCH model is moivaed o accommodae he observed ime-varying reurns volailiies. Table Descripive saisics of daily reurns Parameers Jordan KSA Kuwai Morocco Observaions Mean Median Maximum Minimum Sd. Deviaion Skewness Kurosis Jarque-Bera (.) (.) (.) (.) ADF (.) (.) (.) (.) PP (.) (.) (.) (.) LB-Q (5) (.) (.) (.) (.) LB-Q () (.) (.) (.) (.) LB-Q (5) (.) (.) (.) (.) LB-Q () (.) (.) (.) (.) LB-Q (5) (.) (.) (.) (.) The ARMA(p,q)-GARCH(,)-M approach is used o model he relaionship beween sock reurns and risk. Basically, he echnique consiss of a mean equaion (Eq.) and a variance equaion (Eq.) described as follows: r r r p r p q q log h, () h, () h N, h, (3) where, is he ime scrip, r is he sock marke reurn, h is he GARCH componen, and is a random variable ha depends on he informaion se and has a zero mean and condiional variance h.

4 Finally,,,,,,, and are parameers o be esimaed. The volailiy of he sock marke reurns is measured by he condiional variance h described as a funcion of he squared values of he pas residuals reflecing he ARCH (auoregressive condiionally heeroskedasic) componen and he auoregressive erm h. The parameers and mus saisfy he saionariy condiions such ha,, and ( + ). The laer condiion measures he degree of volailiy persisence. Indeed, he degree of persisence is imporan o deermine he relaionship beween volailiy and reurn since only persisen volailiy explains changes in risk (Devaney, ). In his sudy, he GARCH(,) is chosen since i is parsimonious and allows for long memory in he volailiy process (Devaney, ). The ARMA(p,q)-GARCH(,)-M model is specified based on he Akaike informaion crierion and Bayesian informaion crierion (Green, 8). Thus, he idenified model is ARMA(,)-GARCH(,)-M for Jordan, ARMA(,)-GARCH(,)-M for KSA, and ARMA(,)-GARCH(,)-M for boh Kuwai and Morocco. Equaions and are esimaed using maximum likelihood rouine (Green, 8). The condiional volailiy series h of each marke are shown in Figure, where he x-axis refers o observaions. Jordan x Kuwai x -4.5 KSA x Morocco x Fig.. Volailiy series. Table shows he resuls of he ARMA-GARCH-M model for each marke. For Jordan, i indicaes ha all esimaes of he mean equaion and variance equaion are saisically highly significan a he 5% significance level, excep for he consan erm and he parameer. In paricular, he laer is posiive (.983) bu no significan (p-value =.485). As a resul, he relaionship beween risk and reurn in Jordan sock marke is posiive bu no significan. Similarly, for KSA sock marke all esimaes of he mean equaion and variance equaion are saisically highly significan a he 5% significance level, excep for he consan erm and he parameer. The parameer is posiive (.6) bu no significan (p-value =.43). Thus, he relaionship beween reurn and risk in KSA equiy marke is posiive bu no significan. Finally, all esimaes of he mean equaion and variance equaion are saisically highly significan a he 5% significance level for Kuwai and Morocco. For insance, he regression resuls obained wih Kuwaii daa indicae ha he parameer is posiive (.63) and highly significan (p-value =.6). Similarly, he regression resuls obained wih Moroccan daa indicae ha he parameer is posiive (.694) and highly significan (p-value =.86). Thus, he relaionship beween risk and reurn in boh Kuwaii and Moroccan sock markes is posiive and saisically highly significan. Furhermore, he regression

5 S. Lahmiri / Decision Science Leers (3) 3 resuls indicae ha he sum of he esimaes of and is less han uniy in all markes which is consisen wih heory. Finally, he GARCH effec ( ) is highly significan indicaing ha he sock marke volailiy is ime-varying in all markes. In sum, he empirical findings show ha he relaionship beween risk and reurn in Jordan, KSA, Kowai, and Morocco is posiive and consisen wih heory (Meron, 973, 98), and wih French e al. (987), Campbell and Henschel (99), Bansal and Lundblad (), Girard e al. (), and Xing and Howe (3) who have repored a posiive empirical relaionship. Table Esimaes of he ARMA(p,q)-GARCH(m,n)-M model Parameers Jordan KSA Kuwai Morocco Mean equaion (.54) (.43) (.) (.95) (.) (.) (.) (.6) (.) (.) (.) (.) (.8) (.485) (.43) (.6) (.86) Variance equaion (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) Conclusion The purpose of his empirical sudy is o invesigae he conemporaneous relaionship beween risk measured by condiional volailiy and reurns wih an ARMA-GARCH-in-Mean model in MENA mos acive sock markes including Jordan, KSA, Kuwai, and Morocco. Our resuls provide several insighs. Firs, consisen wih financial heory, he reurns in all sock marke are posiively relaed o risk which is measured by marke volailiy. Second, he relaionship beween risk and reurns in Kuwai and Morocco is saisically highly significan, whils i is no significan in Jordan and KSA. Third, we found srong evidence of GARCH effec in all markes indicaing a ime variaion in he variance of reurn series. In sum, he empirical findings sugges ha invesors are rewarded for aking more risk in hese markes. References Baillie, R., & DeGennaro, P. (99). Sock reurn and volailiy. Journal of Financial and Quaniaive Analysis, 5, 3-4. Bansal, R., & Lundblad, C. (). Marke efficiency, asse reurns, and he size of he risk premium in global equiy markes. Journal of Economerics, 9, Box G.E.P., Jenkins G., & Reinsel, G.C. (994). Time Series Analysis: Forecasing and Conrol. Third ediion. Prenice-Hall.

6 4 Campbell, J.Y., & Henschel, L. (99). No news is good news: an asymmeric model of changing volailiy in sock. Journal of Financial Economics, 3, Curci, R., Grieb, T., & Reyes, M.G. (). Mean and Volailiy Transmission for Lain american Equiy Markes. Sudies in Economics and Finance, (), Devaney, M. (). Time varying risk premia for real esae invesmen russ: A GARCH-M model. The Quarerly Review of Economics and Finance, 4, Dickey, D. A., & Fuller, W.A. (979). Disribuion of he Esimaors for Auoregressive Time Series wih a Uni Roo. Journal of he American Saisical Associaion, 74, Engle, R.F., Lilien, D.M., & Robins, R.P. (987). Esimaing ime varying risk premia in he erm srucure: he ARCH-M model. Economerica, 55, Forgha, N.G. (). An Invesigaion ino he Volailiy and Sock Efficiency in African Sock Exchange Markes. Inernaional Review of Business Research Papers, 8 (5), French, K.R., Schwer, G.W., & Sambaugh, R.F. (987). Expeced sock reurns and volailiy. Journal of Financial Economics, 9, 3-9. Girard, E., Rahman, H., & Zaher, T. (). Ineremporal risk reurn relaionship in he Asian markes around he Asian crisis. Financial Services Review,, Glosen, L., Jagannaha, R., & Runkle, D. (993). The relaionship beween expeced value and he volailiy of he nominal excess reurn on socks. Journal of Finance, 48, Green, W.H. Economeric Analysis. Sevenh ediion. Prenice-Hall, 8. Ljung, G.M., & Box, G.E.P. (978). On a Measure of a Lack of Fi in Time Series Models. Biomerika, 65 (), Meron, R.C. (973). An ineremporal capial asse pricing model. Economerica, 4 (5), Meron, R.C. (98). On esimaing he expeced reurn on he marke. Journal of Financial Economics, 8, Nam, K., Pyun, C.S., & Avard, S.L. (). Asymmeric revering behavior of shor horizon sock reurns: an evidence of sock marke overreacion. Journal of Banking and Finance, 5 (4), Phillips, P.C.B, & Perron, P. (988). Tesing for a Uni Roo in Time Series Regression. Biomerika, 75 (), Xing, X., & Howe, J.S. (3). The empirical relaionship beween risk and reurn: evidence from he UK sock marke. Inernaional Review of Financial Analysis, (3),